Mathematics

If $$\displaystyle \frac{x}{(x-3)(x-2)}= \frac{3}{x-3}+\frac{A}{x-2}$$, then $$A$$= 


ANSWER

$$-2$$


SOLUTION
Given, $$\displaystyle \frac{x}{(x-3)(x-2)}= \frac{3}{x-3}+\frac{A}{x-2}$$         ....(1)
Resolving into partial fraction,
$$\displaystyle \frac { x }{ (x-3)(x-2) } =\frac { A }{ x-2 } +\frac { B }{ x-3 } $$      .....(2)
$$x=A(x-3)+B(x-2)$$
When $$x=3, B=3$$
When $$x=2, A=-2$$
Put these values in (2),
$$\displaystyle \frac { x }{ (x-3)(x-2) } =\frac { -2 }{ x-2 } +\frac { 3 }{ x-3 } $$
Hence, $$A=-2$$
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Single Correct Medium Published on 17th 09, 2020
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